 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| V. M. Sadovskii, "To the analysis of the structure of finite-amplitude transverse shock waves in a plastic medium," Mech. Solids. 38 (6), 31-39 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
31-39 |
| Title |
To the analysis of the structure of finite-amplitude transverse shock waves in a plastic medium |
| Author(s) |
V. M. Sadovskii (Krasnoyarsk) |
| Abstract |
We investigate the structure of transverse dissipative finite amplitude shock waves, with viscous and thermal effects being taken into account. The investigation is based of the theory of flow of a plastic medium under pure shear. The implementability conditions for waves of such type are formulated. It is shown that for materials subject to thermal softening, localization of shear strains in narrow zones with subsequent formation of contact discontinuities is possible. Some results of the numerical analysis of the strain localization process are presented for the case of impulsive loading of a plastic layer.
The problem of description of discontinuous solutions of elastic-plastic shock wave type has been fairly well studied only within the framework of small deformations. A classification of dissipative shock waves in an ideal medium with Mises or Tresca-Saint-Venant plasticity conditions has been performed in [1]. Various versions of linear hardening have been considered in [2, 3]. A model of nonlinear isotropic hardening has been studied in [4]. It turns out that the class of discontinuous solutions substantially depends on both the type of the plasticity condition and the shape (convexity) of the hardening curve of the material.
The expressions for the velocities of propagation of dissipative waves, as well as the relationships between the velocity and stress components, obtained within the framework of the theory of small elastic-plastic deformation are suitable only for the description of small amplitude shock waves. A similar investigation in the case of finite deformations is complicated, since in this case the problem of construction of the integral generalization of the model is essentially more complex. This problem can be solved for some simplified models. However, in such models, part of shock-wave discontinuities determined by the integral generalization method turn out to be unstable with respect to perturbations of the parameters of the medium and, hence, cannot be implemented physically. One of the ways to obtain additional implementability conditions involves studying shock-wave discontinuities on the basis of a thermomechanical model that takes into account the effects of viscosity and heat conduction. The structure of longitudinal finite amplitude shock waves has been considered in [5-7] within the framework of uniaxial deformation. The present paper is devoted to the investigation of the structure of transverse waves within the framework of the model of pure shear in a plastic medium. |
| References |
| 1. | G. I. Bykovtsev and L. D. Kretova, "On the propagation of shock waves in elastic-plastic media,"
PMM [Applied Mathematics and Mechanics], Vol. 36, No. 1, pp. 106-116, 1972. |
| 2. | A. A. Burenin, G. I. Bykovtsev, and V. A. Rychkov,
"Velocity discontinuity surfaces in dynamics of reversibly compressible media,"
in Problems of Mechanics of Continuous Media [in Russian], pp. 116-127,
IAPU DVO RAN, Vladivostok, 1996. |
| 3. | V. M. Sadovskii, "Elastoplastic waves of strong discontinuity in linearly hardening media," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 104-111, 1997. |
| 4. | V. M. Sadovskii, "Regular discontinuities of solutions in dynamics of nonlinearly hardening elastic-plastic media,"
in Problems of Mechanics of Continuous Media and Structural Members [in Russian],
pp. 179-188, IAPU DVO RAN, Vladivostok, 1998. |
| 5. | Ya. A. Pachepskii, "On the structure of shock waves in an elastic-plastic medium,"
PMM [Applied Mathematics and Mechanics], Vol. 37, No. 2, pp. 300-305, 1973. |
| 6. | B. A. Druyanov and E. A. Svyatova, "A problem of the structure of a discontinuity in a hardening plastic medium,"
PMM [Applied Mathematics and Mechanics], Vol. 51, No. 6, pp. 1047-1049, 1987. |
| 7. | V. N. Kukudzhanov, "Investigation of shock wave structure in elasto-viscoplastic bars using asymptotic method,"
Arch. Mech., Vol. 33, No. 5, pp. 739-751, 1981. |
| 8. | V. V. Klyushnikov, "Theory of plasticity: State of the art and
future perspectives,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 102-116, 1993. |
| 9. | L. V. Nikitin, "Post-critical behavior of a softening material,"
Doklady AN, Vol. 342, pp. 487-490, 1995. |
| 10. | V. N. Kukudzhanov,
"On the structure of the strain localization zones
in the case of dynamic loading in the nonlocal theory of plasticity,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 104-114, 1998. |
| 11. | B. E. Pobedrya, "Models in continuum mechanics,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 47-59, 2000. |
|
| Received |
14 May 2001 |
| << Previous article | Volume 38, Issue 6 / 2003 | Next article >> |
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